Tính giá trị của các biểu thức sau:

a) $\sqrt[3]{0,001}$ ;

b) $\sqrt[5]{-32}$ ;

c) $\sqrt[4]{\frac{81}{16}}$ ;

d) $-\sqrt[6]{{100}^3}$;

e) $\sqrt[4]{{\left(\sqrt{3}-2\right)}^4}$ ;

g) $\sqrt[5]{{\left(2-\sqrt{5}\right)}^5}$ .

a) $\sqrt[3]{0,001}=\sqrt[3]{{\left(0,1\right)}^3}=0,1$ .

b) $\sqrt[5]{-32}=\sqrt[5]{(-1).32}=\sqrt[5]{{\left(-1\right)}^5{.2}^5}$

$=\sqrt[5]{{\left(-1\right)}^5}.\sqrt[5]{2^5}=(-1).2=-2$

c) $\sqrt[4]{\frac{81}{16}}=\sqrt[4]{\frac{3^4}{2^4}}=\sqrt[4]{{\left(\frac{3}{2}\right)}^4}=\frac{3}{2}$

d) $-\sqrt[6]{{100}^3}=-\sqrt[6]{{\left({10}^2\right)}^3}=-\sqrt[6]{{10}^6}=-10$

e) $\sqrt[4]{{\left(\sqrt{3}-2\right)}^4}=\left|\sqrt{3}-2\right|=2-\sqrt{3}$

g) $\sqrt[5]{{\left(2-\sqrt{5}\right)}^5}=2-\sqrt{5}$